Over the last few years, several computational techniques have been devised to recover protein complexes from the protein interaction (PPI) networks of organisms. These techniques model dense subnetworks within PPI networks as complexes. However, our comprehensive evaluations revealed that these techniques fail to reconstruct many gold standard complexes that are sparse in the networks (only 71 recovered out of 123 known yeast complexes embedded in a network of 9704 interactions among 1622 proteins). In this work, we propose a novel index called Component-Edge (CE) score to quantitatively measure the notion of complex derivability from PPI networks. Using this index, we theoretically categorize complexes as sparse or dense with respect to a given network. We then devise an algorithm SPARC that selectively employs functional interactions to improve the CE scores of predicted complexes, and thereby elevates many of the sparse complexes to dense. This empowers existing methods to detect these sparse complexes. We demonstrate that our approach is effective in reconstructing significantly many complexes missed previously (104 recovered out of the 123 known complexes or ~47% improvement).
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